PyFolding: Open-Source Graphing, Simulation, and Analysis of the Biophysical Properties of Proteins  Alan R. Lowe, Albert Perez-Riba, Laura S. Itzhaki, Ewan R.G. Main  Biophysical Journal  Volume 114, Issue 3, Pages 516-521 (February 2018) DOI: 10.1016/j.bpj.2017.11.3779 Copyright © 2017 Biophysical Society Terms and Conditions

Figure 1 Work flow example of the fitting linked equations in PyFolding. (A) Unfolding and folding kinetics (chevron plots) showing the distinct fast and slow phases for the three-state folding thermophilic AR protein (tANK) identified in the archaeon Thermoplasma (2) are loaded into PyFolding as chevron objects. (B) Two linked models (functions) are associated with the chevron data. These describe the fast (model 1) and slow phases (model 2) of the chevrons. Certain rate constants and their associated m-values are shared between the two models. The other parameters are “free” and associated and fitted only in the slow-phase model. (C) Global optimization within PyFolding enables simultaneous fitting of the two models with shared parameters to the two respective phases. The resultant fits for the fast (blue dotted line) and slow phases (red solid line) are shown overlaid on the observed data. The residuals show the difference between the slow-phase observations and fit. These calculations can be found in Supporting Material, Jupyter notebook 4. GdmHCl, guanidinium chloride. To see this figure in color, go online. Biophysical Journal 2018 114, 516-521DOI: (10.1016/j.bpj.2017.11.3779) Copyright © 2017 Biophysical Society Terms and Conditions

Figure 2 Work flow example of global optimization of a heteropolymer Ising model in PyFolding. (A) Guanidinium chloride (GdmHCl)-induced equilibrium denaturations of a series of single-helix deletion CTPRn proteins are loaded into PyFolding as EquilibriumDenaturation objects. In the figure, we schematically represent these as individual protein structures corresponding to the smallest in the series (CTPR2-A) up to (dots) the largest (CTPR3) (3). The figures were made with Pymol and individual helices are colored by the user-defined topology used by the Ising model: helix (blue), repeat (black), a mutant repeat (green), or a cap (red). (B) Using PyFolding’s built-in primitive protein folding “domains/modules,” one can define topologies for each protein in the series. Each primitive is a container for several thermodynamic parameters to describe the intrinsic and interfacial stability terms. (C) Using the topologies defined in (B), PyFolding will automatically generate the appropriate partition functions (q) for each protein in the series using a matrix formulation, and share parameters between other proteins in the series. (D) A final global fitting step finds the optimal set of parameters to describe the series. (E) The optimal parameters (and their estimated errors/confidence intervals) for each domain primitive are recovered and output for the user. These calculations can be found in Supporting Material, Jupyter notebook 6. To see this figure in color, go online. Biophysical Journal 2018 114, 516-521DOI: (10.1016/j.bpj.2017.11.3779) Copyright © 2017 Biophysical Society Terms and Conditions